A075875 Triangular numbers that are 3-almost primes.

28, 45, 66, 78, 105, 153, 171, 190, 231, 325, 406, 435, 465, 561, 595, 741, 861, 903, 946, 1378, 1653, 2211, 2278, 2485, 3081, 3655, 3741, 4371, 4465, 4753, 5151, 5253, 5995, 6441, 7021, 7381, 7503, 8515, 8911, 9453, 9591, 10011, 10153, 10585, 11026

Offset: 1

Author

Shyam Sunder Gupta, Oct 19 2002

Keywords

• easy
• nice
• nonn

Examples

			a(1)=28, 28 is a triangular number and 28 = 2*2*7, i.e., is a product of 3 prime factors so is 3-almost prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A000217, A014612, A068443, A128896 (subsequence).

Programs

Mathematica

Select[Accumulate[Range[200]],PrimeOmega[#]==3&] (* Harvey P. Dale, Jul 24 2012 *)

PARI

issemi(n)=bigomega(n)==2
ok(m,n)=if(isprime(m), issemi(n), isprime(n) && issemi(m))
list(lim)=my(v=List()); lim\=1; for(n=7,(sqrt(8*lim+1)-1)\2, if(if(n%2, ok(n,(n+1)/2), ok(n/2,n+1)), listput(v, n*(n+1)/2))); Vec(v) \\ Charles R Greathouse IV, Jun 12 2017

Formula

q:= n-> is(numtheory[bigomega](n)=3):

select(q, [i*(i+1)/2$i=0..200])[]; # Alois P. Heinz, Mar 27 2024